Elicited bid functions in (a)symmetric first-price auctions

Table 7 reports summary statistics on the group distributions of relative errors in each
treatment. Deviations from risk neutral best reply bids are significantly different across types
(at α=.05, two-tailed) only in the LOW treatment; with Strong bidders making larger relative
errors than Weak bidders. Across treatments, Strong bidders deviate significantly more in
LOW than in MIX or SYM; otherwise we find no significant difference in the relative
deviations of Strong and Weak bidders. The relative frequencies of “0 relative errors”
represent less than 10% of all observations for a given type/treatment configuration and we
did not find significant differences across bidders’ types or treatments. In the last 25 rounds of
the experiments, we find no significant difference in the behavior of Strong bidders when the
LOW and MIX treatments are compared, and our conclusions about cross-treatment
comparisons remain unchanged.¹²

Table 7 - Average Relative Deviations from Risk Neutral Best-Reply Bidding.

Such significant cross-treatment differences allude more to type- or environment-specific
patterns than to a pattern that is inherent to bidders’ preferences. The finding of skewed
distributions can equally result from bidders’ heterogeneous behavior, whether it is ad hoc or
rational (as assumed by the CRRA model for heterogeneous bidders of Cox et al., 1988), as
from a homogenous misbehavior such as the miscalculation of winning probabilities and/or a

¹² We also considered bidders’ errors instead of bidders’ relative errors and reached similar conclusions.

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